It is unlikely that damage to the automatic transmission would occur from being struck in the rear passenger tire during an accident. The transmission is located at the front of the vehicle, far from the rear passenger tire. Additionally, the transmission is protected by the vehicle's frame and body, which would absorb most of the impact force from a rear-end collision.
However, it is possible that other damage could occur to the vehicle as a result of being struck in the rear passenger tire, such as damage to the suspension, brakes, or exhaust system. If you have been involved in an accident, it is important to have your vehicle inspected by a qualified mechanic to assess any damage that may have occurred.